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arXiv · 2605.21327

Universal fusion category symmetries on tensor products of infinite-dimensional Hilbert spaces

Ian Bunner·Corey Jones
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Abstract

We show that anyon chains, after stabilizing with infinite-dimensional ancilla spaces, factorize locally as tensor products of infinite-dimensional Hilbert spaces. This implies that any unitary fusion category can be realized as symmetries on a tensor product of infinite-dimensional Hilbert spaces. We then show that any two anyon chains with the same symmetry category are related by a symmetry-compatible locality-preserving unitary after stabilizing with infinite-dimensional ancilla, showing that for a fixed fusion category, there is a single stable equivalence class of symmetry realizations on the lattice via anyon chains. As a corollary of our proof, we show that the physical boundary algebras of Levin-Wen type models are bounded spread isomorphic after stabilization if and only if they have the same bulk topological order.

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Ian Bunner, Corey Jones. 2026-05-20. Universal fusion category symmetries on tensor products of infinite-dimensional Hilbert spaces. https://arxiv.org/abs/2605.21327

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